Power series toolbox. More...

#include <piranha/power_series.hpp>

Inherits Series, and power_series_tag.

Public Member Functions
	power_series ()=default
	Defaulted default constructor.

	power_series (const power_series &)=default
	Defaulted copy constructor.

	power_series (power_series &&)=default
	Defaulted move constructor.

power_series &	operator= (const power_series &other)=default
	Copy assignment operator. More...

power_series &	operator= (power_series &&other)=default
	Move assignment operator. More...

	~power_series ()
	Trivial destructor.

template<typename T = power_series>
degree_type< T >	degree () const
	Total degree. More...

template<typename T = power_series>
ldegree_type< T >	ldegree () const
	Total low degree. More...

template<typename T = power_series>
pdegree_type< T >	degree (const symbol_fset &names) const
	Partial degree. More...

template<typename T = power_series>
pldegree_type< T >	ldegree (const symbol_fset &names) const
	Partial low degree. More...

template<typename T , truncate_degree_enabler< T > = 0>
Derived	truncate_degree (const T &max_degree) const
	Total degree truncation. More...

template<typename T , truncate_pdegree_enabler< T > = 0>
Derived	truncate_degree (const T &max_degree, const symbol_fset &names) const
	Partial degree truncation. More...

Detailed Description

template<typename Series, typename Derived>
class piranha::power_series< Series, Derived >

Power series toolbox.

This toolbox is intended to extend the Series type with properties of formal power series.

Specifically, the toolbox will conditionally augment a Series type by adding methods to query the total and partial (low) degree * of a Series object. Such augmentation takes place if the series' coefficient and/or key types expose methods to query their degree properties (as established by the piranha::has_degree, piranha::key_has_degree and similar type traits), and if the necessary arithmetic operations are supported by the involved types. As an additional requirement, the types returned when querying the degree must be constructible from int, less-than comparable and they must satisfy piranha::is_container_element. If the computation of the degree of a single term involves only C++ integral types, then the computation will be checked for overflow.

This toolbox provides also support for truncation based on the total or partial degree. In addition to the requirements of the degree-querying methods, the truncation methods also require the supplied degree limit to be comparable to the type returned by the degree-querying methods. The truncation methods will recursively truncate the coefficients of the series via the piranha::math::truncate_degree() function.

If the requirements outlined above are not satisfied, the degree-querying and the truncation methods will be disabled.

This class satisfies the piranha::is_series type trait.

Type requirements

Series must satisfy the piranha::is_series type trait,
Derived must derive from power_series of Series and Derived.

Exception safety guarantee

This class provides the same guarantee as Series. The auto-truncation methods offer the basic exception safety guarantee.

Move semantics

Move semantics is equivalent to the move semantics of Series.

Definition at line 314 of file power_series.hpp.

Member Function Documentation

◆ degree() [1/2]

template<typename Series, typename Derived>

template<typename T = power_series>

degree_type<T> piranha::power_series< Series, Derived >::degree ( ) const

inline

Total degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The degree of the series is the maximum degree of its terms. If the series is empty, zero will be returned.

Returns: the total degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the degree of each term, the assignment and less-than operators for the return type.

Definition at line 390 of file power_series.hpp.

◆ degree() [2/2]

template<typename Series, typename Derived>

template<typename T = power_series>

pdegree_type<T> piranha::power_series< Series, Derived >::degree ( const symbol_fset & names ) const

inline

Partial degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The partial degree of the series is the maximum partial degree of its terms. If the series is empty, zero will be returned.

Parameters

names names of the variables to be considered in the computation of the degree.

Returns: the partial degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the degree of each term, the assignment and less-than operators for the return type.

Definition at line 444 of file power_series.hpp.

◆ ldegree() [1/2]

template<typename Series, typename Derived>

template<typename T = power_series>

ldegree_type<T> piranha::power_series< Series, Derived >::ldegree ( ) const

inline

Total low degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The low degree of the series is the minimum low degree of its terms. If the series is empty, zero will be returned.

Returns: the total low degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the low degree of each term, the assignment and less-than operators for the return type.

Definition at line 416 of file power_series.hpp.

◆ ldegree() [2/2]

template<typename Series, typename Derived>

template<typename T = power_series>

pldegree_type<T> piranha::power_series< Series, Derived >::ldegree ( const symbol_fset & names ) const

inline

Partial low degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The partial low degree of the series is the minimum partial low degree of its terms. If the series is empty, zero will be returned.

Parameters

names names of the variables to be considered in the computation of the low degree.

Returns: the partial low degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the low degree of each term, the assignment and less-than operators for the return type.

Definition at line 475 of file power_series.hpp.

◆ operator=() [1/2]

template<typename Series, typename Derived>

power_series& piranha::power_series< Series, Derived >::operator= ( const power_series< Series, Derived > & other )

default

Copy assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

Exceptions

unspecified any exception thrown by the assignment operator of the base class.

◆ operator=() [2/2]

template<typename Series, typename Derived>

power_series& piranha::power_series< Series, Derived >::operator= ( power_series< Series, Derived > && other )

default

Move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ truncate_degree() [1/2]

template<typename Series, typename Derived>

template<typename T , truncate_degree_enabler< T > = 0>

Derived piranha::power_series< Series, Derived >::truncate_degree ( const T & max_degree ) const

inline

Total degree truncation.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

This method can be used to eliminate the parts of a series whose degree is greater than max_degree. This includes the elimination of whole terms, but also the recursive truncation of coefficients via the piranha::math::truncate_degree() function, if supported by the coefficient. It must be noted that, in general, this method is not guaranteed to eliminate all the parts whose degree is greater than max_degree (in particular, in the current implementation there is no truncation implemented for keys - a key is kept as-is or completely eliminated).

Parameters

max_degree maximum allowed total degree.

Returns: the truncated counterpart of this.

Exceptions

unspecified

any exception thrown by:

piranha::math::truncate_degree(), if used,
the constructor of the term type,
the computation and comparison of degree types,
piranha::series::insert().

Definition at line 510 of file power_series.hpp.

◆ truncate_degree() [2/2]

template<typename Series, typename Derived>

template<typename T , truncate_pdegree_enabler< T > = 0>

Derived piranha::power_series< Series, Derived >::truncate_degree	(	const T &	max_degree,
		const symbol_fset &	names
	)		const

inline

Partial degree truncation.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

This method is equivalent to the other overload, the only difference being that the partial degree is considered in the computation.

Parameters

max_degree	maximum allowed partial degree.
names	names of the variables to be considered in the computation of the partial degree.

Returns: the truncated counterpart of this.

Exceptions

unspecified

any exception thrown by:

piranha::math::truncate_degree(), if used,
the constructor of the term type,
the computation and comparison of degree types,
piranha::series::insert().

Definition at line 543 of file power_series.hpp.

The documentation for this class was generated from the following file:

power_series.hpp

Public Member Functions

Detailed Description

template<typename Series, typename Derived> class piranha::power_series< Series, Derived >

Type requirements

Exception safety guarantee

Move semantics

Member Function Documentation

◆ degree() [1/2]

◆ degree() [2/2]

◆ ldegree() [1/2]

◆ ldegree() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ truncate_degree() [1/2]

◆ truncate_degree() [2/2]

template<typename Series, typename Derived>
class piranha::power_series< Series, Derived >